Course Content Packages for Maple T.A. and Möbius - Online Courseware and Assessment Software

# Course Content Packages

Professionally developed courses & content collections, available for immediate use in your own courses

## Calculus I: Differential Calculus

Developed by the University of Waterloo
Available for: Möbius
Pricing and implementation: Contact Maplesoft

This interactive course contains all materials needed for a standard course in Differential Calculus, including functions, limits, derivatives, and an introduction to integration. It provides numerous opportunities for interactive exploration, drill and practice, and assessment, integrated with careful explanations of the materials. While providing a strong mathematical foundation, the emphasis of these courses is on applying calculus to scientific models, making it particularly relatable to students in the sciences.

###### View course outline
FUNCTIONS
- Introduction to Calculus
- Functions
- Combining Functions
- Inverse Functions
- Modelling with Functions
- Exponential Functions
- Trigonometric Functions

LIMITS
- Limits of Sequences
- Instantaneous Velocity
- Limit of a Function at a Point
- Continuity

DERIVATIVES
- The Derivative
- Differentiation Rules
- The Chain Rule
- Implicit Differentiation
APPLICATIONS OF DERIVATIVES
- Modelling with Derivatives
- Exponential Processes
- Linearization
- Newton's Method
- Indeterminate Forms
- Extreme Values
- Shapes of Graphs
- Optimization

INTEGRATION
- Anti-derivatives
- Sigma Notation
- Riemann Sums
- Definite Integrals
- The Fundamental Theorem of Calculus
- Indefinite Integrals
- Integration by Substitution
- Areas Between Curves

## Calculus II: Integral Calculus

Developed by the University of Waterloo
Available for: Möbius
Pricing and implementation: Contact Maplesoft

This interactive course contains all materials needed for a standard course in Integral Calculus, including integration methods, series, differential equations, parametric curves and vector-valued functions, and an introduction to multivariate calculus. It provides numerous opportunities for interactive exploration, drill and practice, and assessment, integrated with careful explanations of the materials. While providing a strong mathematical foundation, the emphasis of these courses is on applying calculus to scientific models, making it particularly relatable to students in the sciences.

###### View course outline
INTEGRATION
- Review of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Integration by Partial Fractions
- Improper Integrals
- Areas and Volumes
- Volumes by Shells
- Arc Length
- Surface Area

SERIES
- Intro to Power Series
- Sequences
- Series
- Integral Test, p-series
- Comparison Test
- Alternating Series, AST, Remainder
- Ratio Test
- Power Series and Convergence
- Working With Power Series
- Taylor Series
- Taylor Polynomials and Taylor's Inequality
- Taylor Approximations in Science

DIFFERENTIAL EQUATIONS
- Intro to Differential Equations
- Linear DEs
- Nonlinear
- Separation of Variables
- Euler's Method and Direction Fields

PARAMETRIC CURVES and VECTOR-VALUED FUNCTIONS
- Parametric Curves
- Polar Coordinates
- Arc Length and Area
- Vector-Valued Functions
- Derivatives: Velocity and Acceleration

MULTIVARIATE CALCULUS
- Multivariable Functions
- 2D, 3D Integrals
- Change of Variables

## College Algebra

Senior Contributing Author: Jay Abramson, Arizona State University
Available for: Möbius
Pricing and implementation: Contact Maplesoft

College Algebra provides a comprehensive exploration of algebraic principles and meets scope and sequence requirements for a typical introductory algebra course. The modular approach and richness of content ensure that this content meets the needs of a variety of courses. College Algebra offers a wealth of examples with detailed, conceptual explanations, building a strong foundation in the material before asking students to apply what they’ve learned.

###### View course outline
This book is available as a free textbook from the OpenStax web site. The Möbius version includes automatically-graded assessment questions and interactive explorations and activities available through the Möbius environment.

Prerequisites
- Real Numbers: Algebra Essentials
- Exponents and Scientific Notation
- Polynomials
- Factoring Polynomials
- Rational Expressions

Equations and Inequalities
- The Rectangular Coordinate Systems and Graphs
- Linear Equations in One Variable
- Models and Applications
- Complex Numbers
- Other Types of Equations
- Linear Inequalities and Absolute Value Inequalities

Functions
- Functions and Function Notation
- Domain and Range
- Rates of Change and Behavior of Graphs
- Composition of Functions
- Transformation of Functions
- Absolute Value Functions
- Inverse Functions

Linear Functions
- Linear Functions
- Modeling with Linear Functions
- Fitting Linear Models to Data

Polynomial and Rational Functions
- Power Functions and Polynomial Functions
- Graphs of Polynomial Functions
- Dividing Polynomials
- Zeros of Polynomial Functions
- Rational Functions
- Modeling Using Variation
Exponential and Logarithmic Functions
- Exponential Functions
- Graphs of Exponential Functions
- Logarithmic Functions
- Graphs of Logarithmic Functions
- Logarithmic Properties
- Exponential and Logarithmic Equations
- Exponential and Logarithmic Models
- Fitting Exponential Models to Data

Systems of Equations and Inequalities
- Systems of Linear Equations: Two Variables
- Systems of Linear Equations: Three Variables
- Systems of Nonlinear Equations and Inequalities: Two Variables
- Partial Fractions
- Matrices and Matrix Operations
- Solving Systems with Gaussian Elimination
- Solving Systems with Inverses
- Solving Systems with Cramer's Rule

Analytic Geometry
- The Ellipse
- The Hyperbola
- The Parabola
- Rotation of Axis
- Conic Sections in Polar Coordinates

Sequences, Probability and Counting Theory
- Sequences and Their Notations
- Arithmetic Sequences
- Geometric Sequences
- Series and Their Notations
- Counting Principles
- Binomial Theorem
- Probability

## Developmental and Intermediate Algebra

Authors: Dr. Shubhangi Stalder, University of Wisconsin Waukesha • Dr. Paul Martin, University of Wisconsin Marathon
Available for: Möbius
Pricing and implementation: Contact Maplesoft

The aim of this course is to teach problem solving skills that will prepare students for college algebra, but also eventually to solve life problems. Inspired by research on math education, brain plasticity, and growth mindsets, it employs both traditional and non-traditional approaches in presenting material.

###### View course outline
Module 0: Mindfulness of Learning Mathematics

Module 1: Introduction to Mathematical Objects
- A Brief History of Numbers
- Number Sets
- Geometric Shapes
- Visualizations of Rational and Decimal Numbers
- Representing Real Numbers on a Number Line and Complex Numbers in the Complex Plane
- Natural Number Exponents and Properties of Exponents
- Negative and Zero Exponents
- Polynomials
- Functions

Module 2: Arithmetic of Algebraic Objects
- Addition as Combining â€œLikeâ€ Units
- Multiplication
- Subtraction as the Inverse of Addition
- Factoring
- Factoring Trinomials and a Geometric Interpretation
- Multiplication of Rational and Radical Expressions
- Division
- Order of Operations
Module 3: Solving Equations and Inequalities
- A Brief History of Equations and Inequalities
- Solving Equations and Inequalities
- Factoring and the Zero Property of Equality

Module 4: Applications and Graphing
- Coordinate Plane Geometry
- Graphing Solutions to Equations in Two Variables
- Graphs of Linear Equations in Two Variables
- Interpreting Graphs and Linear Models
- Other Applications
- Rate Problems
- Using Formulas from a Variety of Fields

## MAA Placement Tests

Developed by the Mathematical Association of America (MAA)
Available for: Möbius, Maple T.A.
Pricing and implementation: Contact Maplesoft

Place your incoming students in the right mathematics courses quickly and painlessly using the renowned Mathematical Association of America (MAA) placement tests offered online exclusively through the Möbius and Maple T.A. testing environments.

## CEGEP

Authors:  Louise Pellerin, enseignante au Département de mathématiques et intervenante en recherché au Cégep de Chicoutimi • Diane Bergeron, coordonnatrice et enseignante dans le programme de Présciences de la santé à la Cité collégiale
Available for: Möbius, Maple T.A.
Pricing and implementation: Contact Maplesoft

Les modules de cours et banques de données pour les cours des mathématiques, créés pour les étudiants francophones du Cégep.